Dual Tableau for Formal Concept Analysis

Abstract

In this chapter we show that an extension of the relational logic RL(1, 1′) can be applied to verification of some logical problems in formal concept analysis, FCA, which originated in [Wil82]. A comprehensive exposition of FCA can be found in [GW99]. A basic data structure in formal concept analysis is a context. It is a two-sorted relational system consisting of a set whose elements are interpreted as objects, a set of features of these objects and a binary relation which holds between an object and a feature whenever the feature is attributed to the object. In the original formulation of FCA the term ‘attribute’ is used instead of ‘feature’, although they are only single-valued attributes. In the more recent developments, FCA distinguishes between single-valued and many-valued attributes. Our terminology is in agreement with that established in relational databases and information systems with incomplete information: an attribute (e.g., color) may have multiple values (e.g., blue, red, etc.), and a feature is a pair ‘attribute-value’ (e.g., being of blue color).